In a simultaneous throw of three coins,what is the probability of getting at least $2$ tails?

Thirty-two persons $X_1, X_2, \ldots, X_{32}$ are randomly seated around a circular table at equal intervals. Two persons $X_i$ and $X_j$ are said to be within earshot of each other if there are at most three persons between them on the minor arc joining $X_i$ and $X_j$. The probability that $X_1$ and $X_3$ are within earshot of each other is:

$X$ speaks truth in $60\%$ and $Y$ in $50\%$ of the cases. The probability that they contradict each other in narrating the same incident is

Two dice are thrown together. The probability that the sum of the numbers is divisible by $2$ or $3$ is

Mr. $A$ has six children and at least one child is a girl. Then,the probability that Mr. $A$ has $3$ boys and $3$ girls is:

$A$ die is loaded such that the probability of throwing the number $i$ is proportional to its reciprocal. Then the probability that $3$ appears in a single throw is